Vibrational dynamics and structure of graphitic amorphous carbon modeled using an embedded-ring approach

The Raman spectrum of graphitic amorphous carbon (g-C) is modeled with simple classical methods, using rings as medium-range structural units. g-C provides a simple [nearly two dimensional (2D) with a single type of atom and one dominant bond type] prototypic example of a large class of continuous random network (CRN) solids where ring or cluster vibrations cannot be decoupled from the network in which they are embedded. We determined the in-plane vibrational modes of n=4, 5, 6, 7, and 8-membered symmetric, planar carbon rings using bond-stretching and bond-angle bending force constants; an additional force constant couples each ring node to the surrounding network. Our results support current models of g-C as small rafts of nearly 2D CRN’s comprised of ≊20% n=5, 60% n=6, and 20% n=7 rings, with very few n=4 and 8 rings. Extensions of the embedded-ring approach to more complex polyatomic and 3D CRN systems and to other probes of vibrational dynamics are discussed.